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Fibonacci sequence

The Fibonacci sequence is the list of numbers such that a number in the sequence is the sum of the of the two sequence numbers.

f(n)=f(n1)+f(n2) f(n) = f(n-1) + f(n-2)

for the starting number equal to 0 or 1 (Be consistant)

Applications

Johannes Kepler observed that the ratio of consecutive Fibonacci numbers converges. "as 5 is to 8 so is 8 to 13, practically, and as 8 is to 13, so is 13 to 21 [almost.]", and concluded that these ratios approach the golden ratio φ